A six-year-old girl who braved hours in the ocean amid 10-metre waves after a yacht sank in the mid-Atlantic later died, Portuguese authorities said.

A French yacht carrying what was believed to be a couple and two children sank after midnight, the Portuguese navy said in a statement.

It was one of four yachts that, separately, ran into trouble during a fierce storm about 900 kilometres south of Portugal's Azores Islands.

The woman and a nine-year-old boy climbed into the yacht's lifeboat and were picked up by a merchant ship.

The navy said a plane threw the man and girl an inflatable lifeboat and they were rescued after dawn, but the girl later died. Officials were unable to give a cause of death or any other information about the family.

The rescue operation occurred during severe weather, which started on Wednesday, the navy said. In total, 12 people were rescued from four yachts in an unusually busy 24 hours for the emergency services.

Aircraft from the Portuguese air force and the US coast guard were diverted from a joint naval exercise after receiving distress calls from the yachts. Two passing merchant ships were also involved.